TSTP Solution File: SET716+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET716+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:26:07 EDT 2023
% Result : Theorem 14.14s 2.92s
% Output : Proof 19.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET716+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.37 % Computer : n003.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 14:41:54 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.70 ________ _____
% 0.22/0.70 ___ __ \_________(_)________________________________
% 0.22/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.70
% 0.22/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.70 (2023-06-19)
% 0.22/0.70
% 0.22/0.70 (c) Philipp Rümmer, 2009-2023
% 0.22/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.70 Amanda Stjerna.
% 0.22/0.70 Free software under BSD-3-Clause.
% 0.22/0.70
% 0.22/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.70
% 0.22/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.73 Running up to 7 provers in parallel.
% 0.61/0.76 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.76 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.76 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.61/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.58/1.53 Prover 1: Preprocessing ...
% 3.58/1.53 Prover 4: Preprocessing ...
% 4.39/1.60 Prover 6: Preprocessing ...
% 4.39/1.60 Prover 5: Preprocessing ...
% 4.39/1.60 Prover 0: Preprocessing ...
% 4.39/1.61 Prover 2: Preprocessing ...
% 4.73/1.61 Prover 3: Preprocessing ...
% 11.25/2.54 Prover 5: Proving ...
% 11.72/2.57 Prover 2: Proving ...
% 11.72/2.65 Prover 3: Constructing countermodel ...
% 11.72/2.65 Prover 1: Constructing countermodel ...
% 11.72/2.66 Prover 6: Proving ...
% 14.14/2.92 Prover 3: proved (2165ms)
% 14.14/2.92
% 14.14/2.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.14/2.92
% 14.14/2.92 Prover 2: stopped
% 14.14/2.92 Prover 5: stopped
% 14.14/2.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.14/2.94 Prover 6: stopped
% 14.14/2.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.14/2.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.14/2.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.63/3.00 Prover 7: Preprocessing ...
% 14.63/3.01 Prover 8: Preprocessing ...
% 14.63/3.04 Prover 10: Preprocessing ...
% 14.63/3.05 Prover 11: Preprocessing ...
% 15.62/3.10 Prover 4: Constructing countermodel ...
% 15.88/3.13 Prover 0: Proving ...
% 15.88/3.13 Prover 0: stopped
% 15.88/3.14 Prover 7: Warning: ignoring some quantifiers
% 15.88/3.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.88/3.17 Prover 7: Constructing countermodel ...
% 15.88/3.18 Prover 13: Preprocessing ...
% 16.40/3.22 Prover 10: Warning: ignoring some quantifiers
% 16.40/3.26 Prover 10: Constructing countermodel ...
% 16.93/3.30 Prover 8: Warning: ignoring some quantifiers
% 16.93/3.31 Prover 8: Constructing countermodel ...
% 16.93/3.31 Prover 13: Warning: ignoring some quantifiers
% 16.93/3.35 Prover 13: Constructing countermodel ...
% 17.68/3.45 Prover 10: gave up
% 17.68/3.48 Prover 1: Found proof (size 126)
% 17.68/3.48 Prover 1: proved (2699ms)
% 17.68/3.48 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 17.68/3.48 Prover 4: stopped
% 17.68/3.48 Prover 13: stopped
% 17.68/3.48 Prover 7: stopped
% 17.68/3.48 Prover 8: stopped
% 17.68/3.48 Prover 11: stopped
% 18.06/3.51 Prover 16: Preprocessing ...
% 18.72/3.53 Prover 16: stopped
% 18.72/3.53
% 18.72/3.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.72/3.53
% 18.72/3.54 % SZS output start Proof for theBenchmark
% 18.72/3.55 Assumptions after simplification:
% 18.72/3.55 ---------------------------------
% 18.72/3.55
% 18.72/3.55 (compose_function)
% 18.72/3.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.72/3.57 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: any] : ( ~ (compose_function(v0,
% 18.72/3.57 v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ $i(v6) | ~
% 18.72/3.57 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9:
% 18.72/3.57 any] : ? [v10: any] : (member(v6, v4) = v10 & member(v5, v2) = v9 & ( ~
% 18.72/3.57 (v10 = 0) | ~ (v9 = 0))) | (( ~ (v8 = 0) | ? [v9: $i] : (apply(v1, v5,
% 18.72/3.57 v9) = 0 & apply(v0, v9, v6) = 0 & member(v9, v3) = 0 & $i(v9))) &
% 18.72/3.57 (v8 = 0 | ! [v9: $i] : ( ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) | ? [v10:
% 18.72/3.57 any] : ? [v11: any] : (apply(v1, v5, v9) = v11 & member(v9, v3) =
% 18.72/3.58 v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))))))
% 18.72/3.58
% 18.72/3.58 (injective)
% 18.72/3.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 18.72/3.58 (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 18.72/3.58 $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 &
% 18.72/3.58 apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 &
% 18.72/3.58 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 18.72/3.58 $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1)
% 18.72/3.58 | ~ $i(v0) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~
% 18.72/3.58 (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~
% 18.72/3.58 $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 18.72/3.58 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8
% 18.72/3.58 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))))
% 18.72/3.58
% 18.72/3.58 (maps)
% 18.72/3.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 18.72/3.58 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 18.72/3.58 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0,
% 18.72/3.58 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) =
% 18.72/3.58 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4)
% 18.72/3.58 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : (
% 18.72/3.58 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 18.72/3.58 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (
% 18.72/3.58 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5)
% 18.72/3.58 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 18.72/3.58 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 18.72/3.58 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0)
% 18.72/3.58 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~
% 18.72/3.58 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 &
% 18.72/3.58 $i(v4)))))
% 18.72/3.58
% 18.72/3.59 (thII07)
% 18.72/3.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 18.72/3.59 $i] : ? [v6: int] : ( ~ (v6 = 0) & injective(v5, v2, v4) = v6 &
% 18.72/3.59 injective(v1, v3, v4) = 0 & injective(v0, v2, v3) = 0 & compose_function(v1,
% 18.72/3.59 v0, v2, v3, v4) = v5 & maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 &
% 18.72/3.59 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 18.72/3.59
% 18.72/3.59 (function-axioms)
% 18.72/3.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 18.72/3.60 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 18.72/3.60 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 18.72/3.60 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.72/3.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.72/3.60 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 18.72/3.60 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.72/3.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.72/3.60 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 18.72/3.60 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.72/3.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.72/3.60 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 18.72/3.60 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.72/3.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 18.72/3.60 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 18.72/3.60 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 18.72/3.60 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.72/3.60 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 18.72/3.60 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.72/3.60 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.72/3.60 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 18.72/3.60 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 18.72/3.60 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 18.72/3.60 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 18.72/3.60 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 18.72/3.60 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.72/3.60 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 18.72/3.60 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.72/3.60 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 18.72/3.60 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 18.72/3.60 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 18.72/3.60 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 18.72/3.60 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.72/3.60 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 18.72/3.60 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 18.72/3.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.72/3.60 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 18.72/3.60 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 18.72/3.60 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 18.72/3.60 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.72/3.60 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 18.72/3.60 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 18.72/3.60 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 18.72/3.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 18.72/3.60 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 18.72/3.60 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.72/3.60 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 18.72/3.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.72/3.60 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 18.72/3.60 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 18.72/3.60 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 18.72/3.60 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 18.72/3.60 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 18.72/3.60 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 18.72/3.60 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.72/3.60 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 18.72/3.60 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.72/3.60 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.72/3.60 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 18.72/3.60 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 18.72/3.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 18.72/3.60 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 18.72/3.60 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 18.72/3.60 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 18.72/3.60 (power_set(v2) = v0))
% 18.72/3.60
% 18.72/3.60 Further assumptions not needed in the proof:
% 18.72/3.60 --------------------------------------------
% 18.72/3.60 compose_predicate, decreasing_function, difference, empty_set, equal_maps,
% 18.72/3.60 equal_set, identity, image2, image3, increasing_function, intersection,
% 18.72/3.60 inverse_function, inverse_image2, inverse_image3, inverse_predicate,
% 18.72/3.60 isomorphism, one_to_one, power_set, product, singleton, subset, sum, surjective,
% 18.72/3.60 union, unordered_pair
% 18.72/3.60
% 18.72/3.60 Those formulas are unsatisfiable:
% 18.72/3.60 ---------------------------------
% 18.72/3.60
% 18.72/3.60 Begin of proof
% 18.72/3.60 |
% 18.72/3.60 | ALPHA: (maps) implies:
% 18.72/3.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) |
% 18.72/3.60 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : !
% 18.72/3.60 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0,
% 18.72/3.60 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6:
% 18.72/3.60 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 18.72/3.60 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~
% 18.72/3.60 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1)
% 18.72/3.60 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 18.72/3.60 | member(v4, v2) = 0 & $i(v4)))))
% 18.72/3.60 |
% 18.72/3.60 | ALPHA: (injective) implies:
% 18.72/3.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) =
% 18.72/3.60 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: $i]
% 18.72/3.60 | : ! [v5: $i] : (v4 = v3 | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0,
% 18.72/3.60 | v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: any]
% 18.72/3.60 | : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4,
% 18.72/3.60 | v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) |
% 18.72/3.60 | ~ (v6 = 0)))))
% 18.72/3.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 18.72/3.61 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.72/3.61 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5,
% 18.72/3.61 | v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5,
% 18.72/3.61 | v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4)))
% 18.72/3.61 |
% 18.72/3.61 | ALPHA: (function-axioms) implies:
% 18.72/3.61 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 18.72/3.61 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 18.72/3.61 | = v0))
% 18.72/3.61 |
% 18.72/3.61 | DELTA: instantiating (thII07) with fresh symbols all_32_0, all_32_1, all_32_2,
% 18.72/3.61 | all_32_3, all_32_4, all_32_5, all_32_6 gives:
% 18.72/3.61 | (5) ~ (all_32_0 = 0) & injective(all_32_1, all_32_4, all_32_2) = all_32_0
% 18.72/3.61 | & injective(all_32_5, all_32_3, all_32_2) = 0 & injective(all_32_6,
% 18.72/3.61 | all_32_4, all_32_3) = 0 & compose_function(all_32_5, all_32_6,
% 18.72/3.61 | all_32_4, all_32_3, all_32_2) = all_32_1 & maps(all_32_5, all_32_3,
% 18.72/3.61 | all_32_2) = 0 & maps(all_32_6, all_32_4, all_32_3) = 0 & $i(all_32_1)
% 18.72/3.61 | & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & $i(all_32_5) &
% 18.72/3.61 | $i(all_32_6)
% 18.72/3.61 |
% 18.72/3.61 | ALPHA: (5) implies:
% 18.72/3.61 | (6) ~ (all_32_0 = 0)
% 18.72/3.61 | (7) $i(all_32_6)
% 18.72/3.61 | (8) $i(all_32_5)
% 18.72/3.61 | (9) $i(all_32_4)
% 18.72/3.61 | (10) $i(all_32_3)
% 18.72/3.61 | (11) $i(all_32_2)
% 18.72/3.61 | (12) $i(all_32_1)
% 18.72/3.61 | (13) maps(all_32_6, all_32_4, all_32_3) = 0
% 18.72/3.61 | (14) compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 18.72/3.61 | all_32_1
% 18.72/3.61 | (15) injective(all_32_6, all_32_4, all_32_3) = 0
% 18.72/3.61 | (16) injective(all_32_5, all_32_3, all_32_2) = 0
% 18.72/3.61 | (17) injective(all_32_1, all_32_4, all_32_2) = all_32_0
% 18.72/3.61 |
% 18.72/3.61 | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_3, simplifying
% 18.72/3.61 | with (7), (9), (10), (13) gives:
% 18.72/3.61 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 18.72/3.61 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) |
% 18.72/3.61 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 18.72/3.61 | [v5: any] : (member(v2, all_32_3) = v5 & member(v1, all_32_3) = v4 &
% 18.72/3.61 | member(v0, all_32_4) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 18.72/3.61 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_4) = 0) | ~
% 18.72/3.61 | $i(v0) | ? [v1: $i] : (apply(all_32_6, v0, v1) = 0 & member(v1,
% 18.72/3.61 | all_32_3) = 0 & $i(v1)))
% 18.72/3.61 |
% 18.72/3.61 | ALPHA: (18) implies:
% 18.72/3.61 | (19) ! [v0: $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | ? [v1: $i]
% 18.72/3.61 | : (apply(all_32_6, v0, v1) = 0 & member(v1, all_32_3) = 0 & $i(v1)))
% 18.72/3.62 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 18.72/3.62 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) |
% 18.72/3.62 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 18.72/3.62 | [v5: any] : (member(v2, all_32_3) = v5 & member(v1, all_32_3) = v4 &
% 18.72/3.62 | member(v0, all_32_4) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 18.72/3.62 | 0))))
% 18.72/3.62 |
% 18.72/3.62 | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3, simplifying
% 18.72/3.62 | with (7), (9), (10), (15) gives:
% 18.72/3.62 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.72/3.62 | (apply(all_32_6, v1, v2) = 0) | ~ (apply(all_32_6, v0, v2) = 0) |
% 18.72/3.62 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 18.72/3.62 | [v5: any] : (member(v2, all_32_3) = v5 & member(v1, all_32_4) = v4 &
% 18.72/3.62 | member(v0, all_32_4) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 18.72/3.62 | 0))))
% 18.72/3.62 |
% 18.72/3.62 | GROUND_INST: instantiating (2) with all_32_5, all_32_3, all_32_2, simplifying
% 18.72/3.62 | with (8), (10), (11), (16) gives:
% 18.72/3.62 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.72/3.62 | (apply(all_32_5, v1, v2) = 0) | ~ (apply(all_32_5, v0, v2) = 0) |
% 18.72/3.62 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 18.72/3.62 | [v5: any] : (member(v2, all_32_2) = v5 & member(v1, all_32_3) = v4 &
% 18.72/3.62 | member(v0, all_32_3) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 18.72/3.62 | 0))))
% 18.72/3.62 |
% 18.72/3.62 | GROUND_INST: instantiating (3) with all_32_1, all_32_4, all_32_2, all_32_0,
% 18.72/3.62 | simplifying with (9), (11), (12), (17) gives:
% 18.72/3.62 | (23) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0)
% 18.72/3.62 | & apply(all_32_1, v1, v2) = 0 & apply(all_32_1, v0, v2) = 0 &
% 18.72/3.62 | member(v2, all_32_2) = 0 & member(v1, all_32_4) = 0 & member(v0,
% 18.72/3.62 | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0))
% 18.72/3.62 |
% 18.72/3.62 | BETA: splitting (23) gives:
% 18.72/3.62 |
% 18.72/3.62 | Case 1:
% 18.72/3.62 | |
% 18.72/3.62 | | (24) all_32_0 = 0
% 18.72/3.62 | |
% 18.72/3.62 | | REDUCE: (6), (24) imply:
% 18.72/3.62 | | (25) $false
% 18.72/3.62 | |
% 18.72/3.62 | | CLOSE: (25) is inconsistent.
% 18.72/3.62 | |
% 18.72/3.62 | Case 2:
% 18.72/3.62 | |
% 18.72/3.62 | | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 18.72/3.62 | | apply(all_32_1, v1, v2) = 0 & apply(all_32_1, v0, v2) = 0 &
% 18.72/3.62 | | member(v2, all_32_2) = 0 & member(v1, all_32_4) = 0 & member(v0,
% 18.72/3.62 | | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0))
% 18.72/3.62 | |
% 18.72/3.62 | | DELTA: instantiating (26) with fresh symbols all_46_0, all_46_1, all_46_2
% 18.72/3.62 | | gives:
% 18.72/3.63 | | (27) ~ (all_46_1 = all_46_2) & apply(all_32_1, all_46_1, all_46_0) = 0 &
% 18.72/3.63 | | apply(all_32_1, all_46_2, all_46_0) = 0 & member(all_46_0, all_32_2)
% 18.72/3.63 | | = 0 & member(all_46_1, all_32_4) = 0 & member(all_46_2, all_32_4) =
% 18.72/3.63 | | 0 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2)
% 18.72/3.63 | |
% 18.72/3.63 | | ALPHA: (27) implies:
% 18.72/3.63 | | (28) ~ (all_46_1 = all_46_2)
% 18.72/3.63 | | (29) $i(all_46_2)
% 18.72/3.63 | | (30) $i(all_46_1)
% 18.72/3.63 | | (31) $i(all_46_0)
% 18.72/3.63 | | (32) member(all_46_2, all_32_4) = 0
% 18.72/3.63 | | (33) member(all_46_1, all_32_4) = 0
% 18.72/3.63 | | (34) member(all_46_0, all_32_2) = 0
% 18.72/3.63 | | (35) apply(all_32_1, all_46_2, all_46_0) = 0
% 18.72/3.63 | | (36) apply(all_32_1, all_46_1, all_46_0) = 0
% 18.72/3.63 | |
% 18.72/3.63 | | GROUND_INST: instantiating (19) with all_46_2, simplifying with (29), (32)
% 18.72/3.63 | | gives:
% 18.72/3.63 | | (37) ? [v0: $i] : (apply(all_32_6, all_46_2, v0) = 0 & member(v0,
% 18.72/3.63 | | all_32_3) = 0 & $i(v0))
% 18.72/3.63 | |
% 18.72/3.63 | | GROUND_INST: instantiating (19) with all_46_1, simplifying with (30), (33)
% 18.72/3.63 | | gives:
% 18.72/3.63 | | (38) ? [v0: $i] : (apply(all_32_6, all_46_1, v0) = 0 & member(v0,
% 18.72/3.63 | | all_32_3) = 0 & $i(v0))
% 18.72/3.63 | |
% 18.72/3.63 | | GROUND_INST: instantiating (compose_function) with all_32_5, all_32_6,
% 18.72/3.63 | | all_32_4, all_32_3, all_32_2, all_46_2, all_46_0, all_32_1, 0,
% 18.72/3.63 | | simplifying with (7), (8), (9), (10), (11), (14), (29), (31),
% 18.72/3.63 | | (35) gives:
% 18.72/3.63 | | (39) ? [v0: any] : ? [v1: any] : (member(all_46_0, all_32_2) = v1 &
% 18.72/3.63 | | member(all_46_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 18.72/3.63 | | ? [v0: $i] : (apply(all_32_5, v0, all_46_0) = 0 & apply(all_32_6,
% 18.72/3.63 | | all_46_2, v0) = 0 & member(v0, all_32_3) = 0 & $i(v0))
% 18.72/3.63 | |
% 19.21/3.63 | | GROUND_INST: instantiating (compose_function) with all_32_5, all_32_6,
% 19.21/3.63 | | all_32_4, all_32_3, all_32_2, all_46_1, all_46_0, all_32_1, 0,
% 19.21/3.63 | | simplifying with (7), (8), (9), (10), (11), (14), (30), (31),
% 19.21/3.63 | | (36) gives:
% 19.21/3.63 | | (40) ? [v0: any] : ? [v1: any] : (member(all_46_0, all_32_2) = v1 &
% 19.21/3.63 | | member(all_46_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 19.21/3.63 | | ? [v0: $i] : (apply(all_32_5, v0, all_46_0) = 0 & apply(all_32_6,
% 19.21/3.63 | | all_46_1, v0) = 0 & member(v0, all_32_3) = 0 & $i(v0))
% 19.21/3.63 | |
% 19.21/3.63 | | DELTA: instantiating (38) with fresh symbol all_53_0 gives:
% 19.21/3.63 | | (41) apply(all_32_6, all_46_1, all_53_0) = 0 & member(all_53_0, all_32_3)
% 19.21/3.63 | | = 0 & $i(all_53_0)
% 19.21/3.63 | |
% 19.21/3.63 | | ALPHA: (41) implies:
% 19.21/3.63 | | (42) $i(all_53_0)
% 19.21/3.63 | | (43) member(all_53_0, all_32_3) = 0
% 19.21/3.63 | | (44) apply(all_32_6, all_46_1, all_53_0) = 0
% 19.21/3.63 | |
% 19.21/3.63 | | DELTA: instantiating (37) with fresh symbol all_55_0 gives:
% 19.21/3.63 | | (45) apply(all_32_6, all_46_2, all_55_0) = 0 & member(all_55_0, all_32_3)
% 19.21/3.63 | | = 0 & $i(all_55_0)
% 19.21/3.63 | |
% 19.21/3.63 | | ALPHA: (45) implies:
% 19.21/3.63 | | (46) $i(all_55_0)
% 19.21/3.63 | | (47) member(all_55_0, all_32_3) = 0
% 19.21/3.63 | | (48) apply(all_32_6, all_46_2, all_55_0) = 0
% 19.21/3.63 | |
% 19.21/3.63 | | BETA: splitting (40) gives:
% 19.21/3.63 | |
% 19.21/3.63 | | Case 1:
% 19.21/3.63 | | |
% 19.21/3.64 | | | (49) ? [v0: any] : ? [v1: any] : (member(all_46_0, all_32_2) = v1 &
% 19.21/3.64 | | | member(all_46_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 19.21/3.64 | | |
% 19.21/3.64 | | | DELTA: instantiating (49) with fresh symbols all_60_0, all_60_1 gives:
% 19.21/3.64 | | | (50) member(all_46_0, all_32_2) = all_60_0 & member(all_46_1, all_32_4)
% 19.21/3.64 | | | = all_60_1 & ( ~ (all_60_0 = 0) | ~ (all_60_1 = 0))
% 19.21/3.64 | | |
% 19.21/3.64 | | | ALPHA: (50) implies:
% 19.21/3.64 | | | (51) member(all_46_1, all_32_4) = all_60_1
% 19.21/3.64 | | | (52) member(all_46_0, all_32_2) = all_60_0
% 19.21/3.64 | | | (53) ~ (all_60_0 = 0) | ~ (all_60_1 = 0)
% 19.21/3.64 | | |
% 19.21/3.64 | | | GROUND_INST: instantiating (4) with 0, all_60_1, all_32_4, all_46_1,
% 19.21/3.64 | | | simplifying with (33), (51) gives:
% 19.21/3.64 | | | (54) all_60_1 = 0
% 19.21/3.64 | | |
% 19.21/3.64 | | | GROUND_INST: instantiating (4) with 0, all_60_0, all_32_2, all_46_0,
% 19.21/3.64 | | | simplifying with (34), (52) gives:
% 19.21/3.64 | | | (55) all_60_0 = 0
% 19.21/3.64 | | |
% 19.21/3.64 | | | BETA: splitting (53) gives:
% 19.21/3.64 | | |
% 19.21/3.64 | | | Case 1:
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | (56) ~ (all_60_0 = 0)
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | REDUCE: (55), (56) imply:
% 19.21/3.64 | | | | (57) $false
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | CLOSE: (57) is inconsistent.
% 19.21/3.64 | | | |
% 19.21/3.64 | | | Case 2:
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | (58) ~ (all_60_1 = 0)
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | REDUCE: (54), (58) imply:
% 19.21/3.64 | | | | (59) $false
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | CLOSE: (59) is inconsistent.
% 19.21/3.64 | | | |
% 19.21/3.64 | | | End of split
% 19.21/3.64 | | |
% 19.21/3.64 | | Case 2:
% 19.21/3.64 | | |
% 19.21/3.64 | | | (60) ? [v0: $i] : (apply(all_32_5, v0, all_46_0) = 0 & apply(all_32_6,
% 19.21/3.64 | | | all_46_1, v0) = 0 & member(v0, all_32_3) = 0 & $i(v0))
% 19.21/3.64 | | |
% 19.21/3.64 | | | DELTA: instantiating (60) with fresh symbol all_60_0 gives:
% 19.21/3.64 | | | (61) apply(all_32_5, all_60_0, all_46_0) = 0 & apply(all_32_6,
% 19.21/3.64 | | | all_46_1, all_60_0) = 0 & member(all_60_0, all_32_3) = 0 &
% 19.21/3.64 | | | $i(all_60_0)
% 19.21/3.64 | | |
% 19.21/3.64 | | | ALPHA: (61) implies:
% 19.21/3.64 | | | (62) $i(all_60_0)
% 19.21/3.64 | | | (63) member(all_60_0, all_32_3) = 0
% 19.21/3.64 | | | (64) apply(all_32_6, all_46_1, all_60_0) = 0
% 19.21/3.64 | | | (65) apply(all_32_5, all_60_0, all_46_0) = 0
% 19.21/3.64 | | |
% 19.21/3.64 | | | BETA: splitting (39) gives:
% 19.21/3.64 | | |
% 19.21/3.64 | | | Case 1:
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | (66) ? [v0: any] : ? [v1: any] : (member(all_46_0, all_32_2) = v1 &
% 19.21/3.64 | | | | member(all_46_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | DELTA: instantiating (66) with fresh symbols all_64_0, all_64_1 gives:
% 19.21/3.64 | | | | (67) member(all_46_0, all_32_2) = all_64_0 & member(all_46_2,
% 19.21/3.64 | | | | all_32_4) = all_64_1 & ( ~ (all_64_0 = 0) | ~ (all_64_1 = 0))
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | ALPHA: (67) implies:
% 19.21/3.64 | | | | (68) member(all_46_2, all_32_4) = all_64_1
% 19.21/3.64 | | | | (69) member(all_46_0, all_32_2) = all_64_0
% 19.21/3.64 | | | | (70) ~ (all_64_0 = 0) | ~ (all_64_1 = 0)
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | GROUND_INST: instantiating (4) with 0, all_64_1, all_32_4, all_46_2,
% 19.21/3.64 | | | | simplifying with (32), (68) gives:
% 19.21/3.64 | | | | (71) all_64_1 = 0
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | GROUND_INST: instantiating (4) with 0, all_64_0, all_32_2, all_46_0,
% 19.21/3.64 | | | | simplifying with (34), (69) gives:
% 19.21/3.64 | | | | (72) all_64_0 = 0
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | BETA: splitting (70) gives:
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | Case 1:
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | | (73) ~ (all_64_0 = 0)
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | | REDUCE: (72), (73) imply:
% 19.21/3.64 | | | | | (74) $false
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | | CLOSE: (74) is inconsistent.
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | Case 2:
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | | (75) ~ (all_64_1 = 0)
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | | REDUCE: (71), (75) imply:
% 19.21/3.64 | | | | | (76) $false
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | | CLOSE: (76) is inconsistent.
% 19.21/3.64 | | | | |
% 19.21/3.64 | | | | End of split
% 19.21/3.64 | | | |
% 19.21/3.64 | | | Case 2:
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | (77) ? [v0: $i] : (apply(all_32_5, v0, all_46_0) = 0 &
% 19.21/3.64 | | | | apply(all_32_6, all_46_2, v0) = 0 & member(v0, all_32_3) = 0 &
% 19.21/3.64 | | | | $i(v0))
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | DELTA: instantiating (77) with fresh symbol all_64_0 gives:
% 19.21/3.64 | | | | (78) apply(all_32_5, all_64_0, all_46_0) = 0 & apply(all_32_6,
% 19.21/3.64 | | | | all_46_2, all_64_0) = 0 & member(all_64_0, all_32_3) = 0 &
% 19.21/3.64 | | | | $i(all_64_0)
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | ALPHA: (78) implies:
% 19.21/3.64 | | | | (79) $i(all_64_0)
% 19.21/3.64 | | | | (80) member(all_64_0, all_32_3) = 0
% 19.21/3.64 | | | | (81) apply(all_32_6, all_46_2, all_64_0) = 0
% 19.21/3.64 | | | | (82) apply(all_32_5, all_64_0, all_46_0) = 0
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | GROUND_INST: instantiating (20) with all_46_2, all_64_0, all_55_0,
% 19.21/3.64 | | | | simplifying with (29), (46), (48), (79), (81) gives:
% 19.21/3.64 | | | | (83) all_64_0 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 19.21/3.64 | | | | : (member(all_64_0, all_32_3) = v1 & member(all_55_0, all_32_3)
% 19.21/3.64 | | | | = v2 & member(all_46_2, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1
% 19.21/3.64 | | | | = 0) | ~ (v0 = 0)))
% 19.21/3.64 | | | |
% 19.21/3.64 | | | | GROUND_INST: instantiating (20) with all_46_1, all_60_0, all_53_0,
% 19.21/3.64 | | | | simplifying with (30), (42), (44), (62), (64) gives:
% 19.21/3.65 | | | | (84) all_60_0 = all_53_0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 19.21/3.65 | | | | : (member(all_60_0, all_32_3) = v1 & member(all_53_0, all_32_3)
% 19.21/3.65 | | | | = v2 & member(all_46_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1
% 19.21/3.65 | | | | = 0) | ~ (v0 = 0)))
% 19.21/3.65 | | | |
% 19.21/3.65 | | | | GROUND_INST: instantiating (22) with all_64_0, all_60_0, all_46_0,
% 19.21/3.65 | | | | simplifying with (31), (62), (65), (79), (82) gives:
% 19.21/3.65 | | | | (85) all_64_0 = all_60_0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 19.21/3.65 | | | | : (member(all_64_0, all_32_3) = v0 & member(all_60_0, all_32_3)
% 19.21/3.65 | | | | = v1 & member(all_46_0, all_32_2) = v2 & ( ~ (v2 = 0) | ~ (v1
% 19.21/3.65 | | | | = 0) | ~ (v0 = 0)))
% 19.21/3.65 | | | |
% 19.21/3.65 | | | | BETA: splitting (84) gives:
% 19.21/3.65 | | | |
% 19.21/3.65 | | | | Case 1:
% 19.21/3.65 | | | | |
% 19.21/3.65 | | | | | (86) all_60_0 = all_53_0
% 19.21/3.65 | | | | |
% 19.21/3.65 | | | | | BETA: splitting (85) gives:
% 19.21/3.65 | | | | |
% 19.21/3.65 | | | | | Case 1:
% 19.21/3.65 | | | | | |
% 19.21/3.65 | | | | | | (87) all_64_0 = all_60_0
% 19.21/3.65 | | | | | |
% 19.21/3.65 | | | | | | COMBINE_EQS: (86), (87) imply:
% 19.21/3.65 | | | | | | (88) all_64_0 = all_53_0
% 19.21/3.65 | | | | | |
% 19.21/3.65 | | | | | | BETA: splitting (83) gives:
% 19.21/3.65 | | | | | |
% 19.21/3.65 | | | | | | Case 1:
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | (89) all_64_0 = all_55_0
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | COMBINE_EQS: (88), (89) imply:
% 19.21/3.65 | | | | | | | (90) all_55_0 = all_53_0
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | SIMP: (90) implies:
% 19.21/3.65 | | | | | | | (91) all_55_0 = all_53_0
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | REDUCE: (48), (91) imply:
% 19.21/3.65 | | | | | | | (92) apply(all_32_6, all_46_2, all_53_0) = 0
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | GROUND_INST: instantiating (21) with all_46_2, all_46_1, all_53_0,
% 19.21/3.65 | | | | | | | simplifying with (29), (30), (42), (44), (92) gives:
% 19.21/3.65 | | | | | | | (93) all_46_1 = all_46_2 | ? [v0: any] : ? [v1: any] : ?
% 19.21/3.65 | | | | | | | [v2: any] : (member(all_53_0, all_32_3) = v2 &
% 19.21/3.65 | | | | | | | member(all_46_1, all_32_4) = v1 & member(all_46_2,
% 19.21/3.65 | | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 19.21/3.65 | | | | | | | 0)))
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | BETA: splitting (93) gives:
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | Case 1:
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | (94) all_46_1 = all_46_2
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | REDUCE: (28), (94) imply:
% 19.21/3.65 | | | | | | | | (95) $false
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | CLOSE: (95) is inconsistent.
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | Case 2:
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | (96) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.21/3.65 | | | | | | | | (member(all_53_0, all_32_3) = v2 & member(all_46_1,
% 19.21/3.65 | | | | | | | | all_32_4) = v1 & member(all_46_2, all_32_4) = v0 & (
% 19.21/3.65 | | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | DELTA: instantiating (96) with fresh symbols all_114_0,
% 19.21/3.65 | | | | | | | | all_114_1, all_114_2 gives:
% 19.21/3.65 | | | | | | | | (97) member(all_53_0, all_32_3) = all_114_0 &
% 19.21/3.65 | | | | | | | | member(all_46_1, all_32_4) = all_114_1 &
% 19.21/3.65 | | | | | | | | member(all_46_2, all_32_4) = all_114_2 & ( ~ (all_114_0
% 19.21/3.65 | | | | | | | | = 0) | ~ (all_114_1 = 0) | ~ (all_114_2 = 0))
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | ALPHA: (97) implies:
% 19.21/3.65 | | | | | | | | (98) member(all_46_2, all_32_4) = all_114_2
% 19.21/3.65 | | | | | | | | (99) member(all_46_1, all_32_4) = all_114_1
% 19.21/3.65 | | | | | | | | (100) member(all_53_0, all_32_3) = all_114_0
% 19.21/3.65 | | | | | | | | (101) ~ (all_114_0 = 0) | ~ (all_114_1 = 0) | ~ (all_114_2
% 19.21/3.65 | | | | | | | | = 0)
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | GROUND_INST: instantiating (4) with 0, all_114_2, all_32_4,
% 19.21/3.65 | | | | | | | | all_46_2, simplifying with (32), (98) gives:
% 19.21/3.65 | | | | | | | | (102) all_114_2 = 0
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | GROUND_INST: instantiating (4) with 0, all_114_1, all_32_4,
% 19.21/3.65 | | | | | | | | all_46_1, simplifying with (33), (99) gives:
% 19.21/3.65 | | | | | | | | (103) all_114_1 = 0
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | GROUND_INST: instantiating (4) with 0, all_114_0, all_32_3,
% 19.21/3.65 | | | | | | | | all_53_0, simplifying with (43), (100) gives:
% 19.21/3.65 | | | | | | | | (104) all_114_0 = 0
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | BETA: splitting (101) gives:
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | | Case 1:
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | | (105) ~ (all_114_0 = 0)
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | | REDUCE: (104), (105) imply:
% 19.21/3.65 | | | | | | | | | (106) $false
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | | CLOSE: (106) is inconsistent.
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | Case 2:
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | | (107) ~ (all_114_1 = 0) | ~ (all_114_2 = 0)
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | | BETA: splitting (107) gives:
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | | Case 1:
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | | (108) ~ (all_114_1 = 0)
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | | REDUCE: (103), (108) imply:
% 19.21/3.65 | | | | | | | | | | (109) $false
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | | CLOSE: (109) is inconsistent.
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | Case 2:
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | | (110) ~ (all_114_2 = 0)
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | | REDUCE: (102), (110) imply:
% 19.21/3.65 | | | | | | | | | | (111) $false
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | | CLOSE: (111) is inconsistent.
% 19.21/3.65 | | | | | | | | | |
% 19.21/3.65 | | | | | | | | | End of split
% 19.21/3.65 | | | | | | | | |
% 19.21/3.65 | | | | | | | | End of split
% 19.21/3.65 | | | | | | | |
% 19.21/3.65 | | | | | | | End of split
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | Case 2:
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | (112) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.21/3.65 | | | | | | | (member(all_64_0, all_32_3) = v1 & member(all_55_0,
% 19.21/3.65 | | | | | | | all_32_3) = v2 & member(all_46_2, all_32_4) = v0 & (
% 19.21/3.65 | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | DELTA: instantiating (112) with fresh symbols all_91_0, all_91_1,
% 19.21/3.65 | | | | | | | all_91_2 gives:
% 19.21/3.65 | | | | | | | (113) member(all_64_0, all_32_3) = all_91_1 & member(all_55_0,
% 19.21/3.65 | | | | | | | all_32_3) = all_91_0 & member(all_46_2, all_32_4) =
% 19.21/3.65 | | | | | | | all_91_2 & ( ~ (all_91_0 = 0) | ~ (all_91_1 = 0) | ~
% 19.21/3.65 | | | | | | | (all_91_2 = 0))
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | ALPHA: (113) implies:
% 19.21/3.65 | | | | | | | (114) member(all_46_2, all_32_4) = all_91_2
% 19.21/3.65 | | | | | | | (115) member(all_55_0, all_32_3) = all_91_0
% 19.21/3.65 | | | | | | | (116) member(all_64_0, all_32_3) = all_91_1
% 19.21/3.65 | | | | | | | (117) ~ (all_91_0 = 0) | ~ (all_91_1 = 0) | ~ (all_91_2 = 0)
% 19.21/3.65 | | | | | | |
% 19.21/3.65 | | | | | | | REDUCE: (88), (116) imply:
% 19.21/3.65 | | | | | | | (118) member(all_53_0, all_32_3) = all_91_1
% 19.21/3.65 | | | | | | |
% 19.21/3.66 | | | | | | | GROUND_INST: instantiating (4) with 0, all_91_2, all_32_4,
% 19.21/3.66 | | | | | | | all_46_2, simplifying with (32), (114) gives:
% 19.21/3.66 | | | | | | | (119) all_91_2 = 0
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | GROUND_INST: instantiating (4) with 0, all_91_1, all_32_3,
% 19.21/3.66 | | | | | | | all_53_0, simplifying with (43), (118) gives:
% 19.21/3.66 | | | | | | | (120) all_91_1 = 0
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | GROUND_INST: instantiating (4) with 0, all_91_0, all_32_3,
% 19.21/3.66 | | | | | | | all_55_0, simplifying with (47), (115) gives:
% 19.21/3.66 | | | | | | | (121) all_91_0 = 0
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | BETA: splitting (117) gives:
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | Case 1:
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | (122) ~ (all_91_0 = 0)
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | REDUCE: (121), (122) imply:
% 19.21/3.66 | | | | | | | | (123) $false
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | CLOSE: (123) is inconsistent.
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | Case 2:
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | (124) ~ (all_91_1 = 0) | ~ (all_91_2 = 0)
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | BETA: splitting (124) gives:
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | Case 1:
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | | (125) ~ (all_91_1 = 0)
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | | REDUCE: (120), (125) imply:
% 19.21/3.66 | | | | | | | | | (126) $false
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | | CLOSE: (126) is inconsistent.
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | Case 2:
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | | (127) ~ (all_91_2 = 0)
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | | REDUCE: (119), (127) imply:
% 19.21/3.66 | | | | | | | | | (128) $false
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | | CLOSE: (128) is inconsistent.
% 19.21/3.66 | | | | | | | | |
% 19.21/3.66 | | | | | | | | End of split
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | End of split
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | End of split
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | Case 2:
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | (129) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.21/3.66 | | | | | | (member(all_64_0, all_32_3) = v0 & member(all_60_0,
% 19.21/3.66 | | | | | | all_32_3) = v1 & member(all_46_0, all_32_2) = v2 & ( ~
% 19.21/3.66 | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | DELTA: instantiating (129) with fresh symbols all_87_0, all_87_1,
% 19.21/3.66 | | | | | | all_87_2 gives:
% 19.21/3.66 | | | | | | (130) member(all_64_0, all_32_3) = all_87_2 & member(all_60_0,
% 19.21/3.66 | | | | | | all_32_3) = all_87_1 & member(all_46_0, all_32_2) =
% 19.21/3.66 | | | | | | all_87_0 & ( ~ (all_87_0 = 0) | ~ (all_87_1 = 0) | ~
% 19.21/3.66 | | | | | | (all_87_2 = 0))
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | ALPHA: (130) implies:
% 19.21/3.66 | | | | | | (131) member(all_46_0, all_32_2) = all_87_0
% 19.21/3.66 | | | | | | (132) member(all_60_0, all_32_3) = all_87_1
% 19.21/3.66 | | | | | | (133) member(all_64_0, all_32_3) = all_87_2
% 19.21/3.66 | | | | | | (134) ~ (all_87_0 = 0) | ~ (all_87_1 = 0) | ~ (all_87_2 = 0)
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | REDUCE: (86), (132) imply:
% 19.21/3.66 | | | | | | (135) member(all_53_0, all_32_3) = all_87_1
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | GROUND_INST: instantiating (4) with 0, all_87_0, all_32_2, all_46_0,
% 19.21/3.66 | | | | | | simplifying with (34), (131) gives:
% 19.21/3.66 | | | | | | (136) all_87_0 = 0
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | GROUND_INST: instantiating (4) with 0, all_87_1, all_32_3, all_53_0,
% 19.21/3.66 | | | | | | simplifying with (43), (135) gives:
% 19.21/3.66 | | | | | | (137) all_87_1 = 0
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | GROUND_INST: instantiating (4) with 0, all_87_2, all_32_3, all_64_0,
% 19.21/3.66 | | | | | | simplifying with (80), (133) gives:
% 19.21/3.66 | | | | | | (138) all_87_2 = 0
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | BETA: splitting (134) gives:
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | Case 1:
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | (139) ~ (all_87_0 = 0)
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | REDUCE: (136), (139) imply:
% 19.21/3.66 | | | | | | | (140) $false
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | CLOSE: (140) is inconsistent.
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | Case 2:
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | (141) ~ (all_87_1 = 0) | ~ (all_87_2 = 0)
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | BETA: splitting (141) gives:
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | Case 1:
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | (142) ~ (all_87_1 = 0)
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | REDUCE: (137), (142) imply:
% 19.21/3.66 | | | | | | | | (143) $false
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | CLOSE: (143) is inconsistent.
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | Case 2:
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | (144) ~ (all_87_2 = 0)
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | REDUCE: (138), (144) imply:
% 19.21/3.66 | | | | | | | | (145) $false
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | | CLOSE: (145) is inconsistent.
% 19.21/3.66 | | | | | | | |
% 19.21/3.66 | | | | | | | End of split
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | End of split
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | End of split
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | Case 2:
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | (146) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 19.21/3.66 | | | | | (member(all_60_0, all_32_3) = v1 & member(all_53_0, all_32_3)
% 19.21/3.66 | | | | | = v2 & member(all_46_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~
% 19.21/3.66 | | | | | (v1 = 0) | ~ (v0 = 0)))
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | DELTA: instantiating (146) with fresh symbols all_83_0, all_83_1,
% 19.21/3.66 | | | | | all_83_2 gives:
% 19.21/3.66 | | | | | (147) member(all_60_0, all_32_3) = all_83_1 & member(all_53_0,
% 19.21/3.66 | | | | | all_32_3) = all_83_0 & member(all_46_1, all_32_4) =
% 19.21/3.66 | | | | | all_83_2 & ( ~ (all_83_0 = 0) | ~ (all_83_1 = 0) | ~
% 19.21/3.66 | | | | | (all_83_2 = 0))
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | ALPHA: (147) implies:
% 19.21/3.66 | | | | | (148) member(all_46_1, all_32_4) = all_83_2
% 19.21/3.66 | | | | | (149) member(all_53_0, all_32_3) = all_83_0
% 19.21/3.66 | | | | | (150) member(all_60_0, all_32_3) = all_83_1
% 19.21/3.66 | | | | | (151) ~ (all_83_0 = 0) | ~ (all_83_1 = 0) | ~ (all_83_2 = 0)
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | GROUND_INST: instantiating (4) with 0, all_83_2, all_32_4, all_46_1,
% 19.21/3.66 | | | | | simplifying with (33), (148) gives:
% 19.21/3.66 | | | | | (152) all_83_2 = 0
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | GROUND_INST: instantiating (4) with 0, all_83_0, all_32_3, all_53_0,
% 19.21/3.66 | | | | | simplifying with (43), (149) gives:
% 19.21/3.66 | | | | | (153) all_83_0 = 0
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | GROUND_INST: instantiating (4) with 0, all_83_1, all_32_3, all_60_0,
% 19.21/3.66 | | | | | simplifying with (63), (150) gives:
% 19.21/3.66 | | | | | (154) all_83_1 = 0
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | BETA: splitting (151) gives:
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | | Case 1:
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | (155) ~ (all_83_0 = 0)
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | REDUCE: (153), (155) imply:
% 19.21/3.66 | | | | | | (156) $false
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | CLOSE: (156) is inconsistent.
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | Case 2:
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | (157) ~ (all_83_1 = 0) | ~ (all_83_2 = 0)
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | BETA: splitting (157) gives:
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | | Case 1:
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | (158) ~ (all_83_1 = 0)
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | REDUCE: (154), (158) imply:
% 19.21/3.66 | | | | | | | (159) $false
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | CLOSE: (159) is inconsistent.
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | Case 2:
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | (160) ~ (all_83_2 = 0)
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | REDUCE: (152), (160) imply:
% 19.21/3.66 | | | | | | | (161) $false
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | | CLOSE: (161) is inconsistent.
% 19.21/3.66 | | | | | | |
% 19.21/3.66 | | | | | | End of split
% 19.21/3.66 | | | | | |
% 19.21/3.66 | | | | | End of split
% 19.21/3.66 | | | | |
% 19.21/3.66 | | | | End of split
% 19.21/3.66 | | | |
% 19.21/3.66 | | | End of split
% 19.21/3.66 | | |
% 19.21/3.66 | | End of split
% 19.21/3.66 | |
% 19.21/3.66 | End of split
% 19.21/3.66 |
% 19.21/3.66 End of proof
% 19.21/3.67 % SZS output end Proof for theBenchmark
% 19.21/3.67
% 19.21/3.67 2959ms
%------------------------------------------------------------------------------